Lucas Saorín, Pascual

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Lucas Saorín, Pascual

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Lucas Saorín, Pascual

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Universidad de Murcia. Departamento de Matemáticas

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Open Access
A generalization of the notion of helix
(Scientific and Technological Research Council of Turkey, 2023) Lucas Saorín, Pascual; Ortega Yagües, José Antonio; Matemáticas
In this paper we generalize the notion of helix in the three-dimensional Euclidean space, which we define as that curve $\alpha$ for which there is an $F$-constant vector field $W$ along $\alpha$ that forms a constant angle with a fixed direction $V$ (called an axis of the helix). We find the natural equation and the geometric integration of helices $\alpha$ where the $F$-constant vector field $W$ is orthogonal to its axis.
Open Access
L1-2-Type Surfaces in 3-Dimensional De Sitter and Anti De Sitter Spaces
(Springer, 2023-06-01) García Martínez, S. Carolina; Lucas Saorín, Pascual; Ramírez Ospina, H. Fabián; Matemáticas
Let be an orientable surface immersed in the De Sitter space or anti de Sitter space . In the case that is of -2-type we prove that the following conditions are equivalent to each other: has a constant principal curvature; has constant mean curvature; has constant second mean curvature. As a consequence, we also show that an -2-type surface is either an open portion of a standard pseudo-Riemannian product, or a B-scroll over a null curve, or else its mean curvature, its Gaussian curvature and its principal curvatures are all non-constant.
Open Access
Concircular helices and concircular surfaces in Euclidean 3-space R3
(Universidad de Hacettepe, 2023) Lucas Saorín, Pascual; Ortega Yagües, José Antonio; Matemáticas
In this paper we characterize concircular helices in R3 by means of a differential equation involving their curvature and torsion. We find a full description of concircular surfaces in R3 as a special family of ruled surfaces, and we show that M ⊂ R3 is a proper concircular surface if and only if either M is parallel to a conical surface or M is the normal surface to a spherical curve. Finally, we characterize the concircular helices as geodesics of concircular surfaces.
Open Access
A property that characterizes the Enneper surface and helix surfaces
(Springer, 2024-06-29) Lucas Saorín, Pascual; Otega Yagües, José Antonio; Matemáticas
The main goal of this paper is to show that helix surfaces and the Enneper surface are theonly surfaces in the 3-dimensional Euclidean space R3 whose isogonal lines are generalizedhelices and pseudo-geodesic lines.
Open Access
Concircular hypersurfaces and concircular helices inspace forms
(Springer, 2023-08-23) Lucas Saorín, Pascual; Ortega Yagües, José Antonio; Matemáticas
In this paper, we find a full description of concircular hypersurfaces in spaceforms as a special family of ruled hypersurfaces. We also characterize concircularhelices in 3-dimensional space forms by means of a differential equation involving theconcircular factor and their curvature and torsion, and we show that the concircularhelices are precisely the geodesics of the concircular surfaces.